---
title: "Reciprocity theorem"
subject: "Basic Electrical Engineering"
chapter: 3
key: "semester_1/basic_electrical_engineering:reciprocity-theorem-state"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/reciprocity-theorem-state
site: BCT Engineering
---

# Reciprocity theorem

Basic Electrical Engineering · Chapter 3: Network Theorems

- Asked in: 2067 Asoj, 4 marks
- Video: [Reciprocity Theorem - Theory and Solved Example  (w subtitles)](https://www.youtube.com/watch?v=CaIcjb2U5hU) — EE Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/reciprocity-theorem-state
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-3

## Question

Describe briefly: Reciprocity Theorem

## Short answer

In a linear, bilateral, single-source network, interchanging the position of the voltage source and the point of current measurement yields the same current. The ratio of excitation to response is symmetric.

## Answer

#### Statement
**Reciprocity theorem:** in a linear, bilateral, passive network with a **single source**, if a voltage source V placed in one branch produces a current I in another branch, then the same source V placed in the second branch produces the same current I in the first branch. Equivalently, the ratio V/I (transfer resistance) is the same when the source and the measuring point are interchanged.

```text
 Case 1: source in branch 1       Case 2: source in branch 2
  (V) in branch 1 --> I in 2       (V) in branch 2 --> same I in 1
```

#### Conditions
- The network must be linear and bilateral (resistors, inductors, capacitors; no semiconductors).
- Only one source is active at a time.
- The polarity of the source and the direction of the measured current must be kept consistent in both cases.

#### Example
A 10 V source with 2 Ω in series feeds a 3 Ω shunt, and a 2 Ω load is connected beyond it.
- Case 1: source in the input branch. Total R = 2 + (3 ∥ 2) = 3.2 Ω, I = 3.125 A. Voltage across the 3 Ω ∥ 2 Ω part = 3.125 × 1.2 = 3.75 V, so the current in the output 2 Ω = 1.875 A.
- Case 2: the 10 V source is moved into the output branch (in series with the output 2 Ω), and its old place in the input branch is replaced by a short circuit. The input 2 Ω stays in the circuit as the measured branch. Total R = 2 + (3 ∥ 2) = 3.2 Ω, I = 3.125 A. Voltage across the 3 Ω ∥ 2 Ω part = 3.75 V, so the current in the input 2 Ω = 1.875 A.

Both currents are equal (1.875 A), so the theorem is verified. It does not apply to circuits with dependent sources or non-linear elements.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the reciprocity theorem state?
   A. A source V in branch 1 producing I in branch 2 will produce the same I in branch 1 if placed in branch 2
   B. Power in each branch is equal
   C. The source and response always add
   D. The response doubles when the source is moved
   Answer: A. Valid for single-source linear bilateral passive networks; transfer resistance V/I is unchanged by interchange. (Key point: Statement)

2. Which condition is required for reciprocity?
   A. Several sources at once
   B. Network containing dependent sources
   C. Non-linear devices such as diodes
   D. Linear, bilateral network with only one source active
   Answer: D. It fails with semiconductors, dependent sources or multiple sources. (Key point: Conditions)

3. In the worked example, what verifies the theorem?
   A. The two voltages are 10 V and 5 V
   B. The current in the output branch with the source at input and in the input branch with the source at output are both 1.875 A
   C. Both total currents are 3.125 A only
   D. The input current is 3.75 A in both cases
   Answer: B. Both cases give 1.875 A in the other branch, so interchange leaves the current unchanged. (Key point: Example check)

## Related in Basic Electrical Engineering

- [State and verify reciprocity theorem](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Areciprocity-theorem-verify-cd) — Basic Electrical Engineering, chapter 3

## Related in other subjects

- [Reciprocity theorem for antennas](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Areciprocity-theorem) — Propagation and Antenna, chapter 1, asked 7×
- [Stiffness, flexibility and reciprocity theorem](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Amatrix-equations-flexibility-reciprocity) — Theory of Mechanism and Machine II, chapter 8